Mathlib Map

Theorems · Definition · ring theory

NonUnitalSubring.center

(R : Type u) → [inst : NonUnitalNonAssocRing R] → NonUnitalSubring R

The center of a ring R is the set of elements that commute with everything in R

Defined in
Mathlib.RingTheory.NonUnitalSubring.Basic
Cited by
13 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonUnitalNonAssocRing

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NonUnitalSubring.centerCongr · cited by 2NonUnitalSubring.centerCo…NonUnitalSubring.centerToMulOpposite · cited by 2NonUnitalSubring.centerTo…NonUnitalSubalgebra.center_toNonUnitalSubring · cited by 0NonUnitalSubalgebra.cente…NonUnitalSubring.coe_center · cited by 0NonUnitalSubring.coe_cent…NonUnitalSubring.centerCongr_apply_coe · cited by 0NonUnitalSubring.centerCo…NonUnitalSubring.centerCongr_symm_apply_coe · cited by 0NonUnitalSubring.centerCo…NonUnitalSubring.centerToMulOpposite_apply_coe · cited by 0NonUnitalSubring.centerTo…NonUnitalSubring.centerToMulOpposite_symm_apply_coe · cited by 0NonUnitalSubring.centerTo…NonUnitalSubring.center_eq_top · cited by 0NonUnitalSubring.center_e…NonUnitalSubring.center_le_centralizer · cited by 0NonUnitalSubring.center_l…NonUnitalSubring.center_prod · cited by 0NonUnitalSubring.center_p…NonUnitalSubring.center_toNonUnitalSubsemiring · cited by 0NonUnitalSubring.center_t…NonUnitalSubring.mem_center_iff · cited by 0NonUnitalSubring.mem_cent…NonUnitalSubring.centralizer_eq_top_iff_subset · cited by 0NonUnitalSubring.centrali…NonUnitalSubring.centralizer_univ · cited by 0NonUnitalSubring.centrali…NonUnitalNonAssocRing · cited by 354NonUnitalNonAssocRingNonUnitalSubsemiring · cited by 201NonUnitalSubsemiringNonUnitalSubring · cited by 185NonUnitalSubringNonUnitalSubsemiring.center · cited by 22NonUnitalSubsemiring.cent…Set.neg_mem_center · cited by 0Set.neg_mem_centerNonUnitalSubring.centerCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by15

Results whose statement or proof uses this declaration.